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Is the Maximum Strain Theory a non-interactive failure criterion?

Failure criteria for composite materials are usually classified in two categories: non-interactive and interactive theories. In literature, you can find that the main non-interactive failure criteria are the Maximum Stress Theory and the Maximum Strain Theory. However, one question arises: is the second one a non-interactive theory in reality? Let’s figure it out.

To begin with, a non-interactive failure criterion is that one which only takes into account the effect of one stress or strain component for each failure condition. In other words, it does not consider any interaction between the different components. For example, the Maximum Stress Theory considers that the material fails when one of the stress components reaches a maximum value. Hence, considering a sample loaded in tension:

Where subindex 1 refers to the fibre direction and 2 corresponds to the transverse direction. When the stress reaches the limit value (measured experimentally under uniaxial stress conditions), the material fails. It is clear how in that failure criterion only one stress component is considered for each condition.

Let’s have a look at the Maximum Strain Theory, which basically states the same principle as the Maximum Stress Theory, changing the term “stress” for “strain”. Then, considering again a lamina loaded in tension:

Therefore, when uniaxial loading is considered, these two theories can be correlated:

So far, both of them are, obviously, non-interactive theories. But, what happens when biaxial loading is considered? Let me show you.

According to the Maximum Stress Theory, failure occurs when:

On the other hand, the Maximum Strain Theory predicts failure when:

Now it is observed how the Maximum Strain Theory is non-interactive in terms of strain but interactive in terms of stress, since two stress components are present in each expression.

I hope that from now on you will think carefully when classifying the Maximum Strain Theory as a non-interactive failure criterion. We should always specify this fact in order to avoid confusions!